Dark Matter and Dark EnergyDark Matter and Dark Energy

Rocky I: Evidence for dark matter and dark energy Rocky II: Dark matter candidatesRocky III: Dark energy reloaded

SLAC Summer Institute, August 2003Rocky Kolb, Fermilab & The University of Chicago

ν

ν

ν

Heavy Elements: Ω=0.0003

Cold Dark Matter: Ω=0.25

Dark Energy (Λ): Ω=0.70

Stars:Ω=0.005

Free H & He:Ω=0.04

CRITICAL

TOTAL 1i iρ ρΩ ≡

Ω =

Cosmic PieCosmic PieCosmic Pie

ΛCDMΛΛCDMCDM

Neutrinos (ν): Ω=0.0047

What We “Know”What We “Know”What We “Know”The matter density is dominated by cold dark matter, which we know nothing about!

, which we know nothing about!

, which we know less than nothing about!

The universe is dominated by a cosmological term(dark energy, funny energy, quintessence, polenta, cosmological constant, cosmo-illogical constant, ….)

The perturbations arise from inflationary dynamics, which depends on particle physics at high energies

, EWK doesn’t seem to work….GUT scenarios are not simple!

The baryon asymmetry arises in the GUT or EWK era throughB, CP, and equilibrium violation (Sakharov’s ingredients)

***

* It ain’t what you don’t know, it’s what you know that ain’t so!

We’re almost free, I just felt the first drops of rain

CDMΛ

Do we have concordance-a standard cosmological model?*

Do we have concordanceDo we have concordance--a standard cosmological model?*a standard cosmological model?*

* Do we want one? The goal is not concordance, but correctness!

• Radiation• Neutrinos• Dark matter• Dark baryons• Dark energy• Inflation• Baryo/leptogenesis

• Hypotheses?• Saving the appearances?

• Epicycles?

If I had been present at creation, I would have suggested a simpler scheme.

- Alfonse the Wise

Epicycle I – InflationEpicycle I Epicycle I –– InflationInflation

density perturbations, gravitational waves,(particle production in the expanding universe)

eternal inflation, wave function of the universe,did the universe have a beginning ????

defrosting, heating, preheating, reheating, baryogenesis, phase transitions, dark matter,(particle production in the expanding universe)

1. Beginning

2. Middle

3. End

Inflation, as a whole, can be divided into three parts

Epicycle II – Dark matterEpicycle II Epicycle II –– Dark matterDark matterWhat is dark matter?

“In questions like this, truth is only to be had by laying together many variations of error.”

-- Virginia WolfA Room of Ones Own

Font & NavarroFrenk, White, . . .

Epicycle III – Dark EnergyEpicycle III Epicycle III –– Dark EnergyDark Energy

“In questions like this, truth is only to be had by laying together many variations of error.”

-- Virginia WolfA Room of Ones Own

What is the nature of dark energy

The universe observedThe universe observedThe universe observed• Cosmological parameters:

• Power spectra:

• “Standard model”: Dark Energy and Dark matter

( )

0

0

TOTAL

0

0

Hubble's constant deceleration parameter the cosmic food chain

, , , , , , .....

age of the universe temperature of the univer

i

M B

Hq

tT

γ νΛ

→→

Ω →

Ω Ω Ω Ω Ω Ω

→→ se

( ), lP k C

CDMΛ

Big-Bang TheoryBigBig--Bang TheoryBang Theory

( )

22 2 2 2 2

2

cosmic scale factor0, 1

( )1

a tk

drds dt a t r dkr

=

= ±

= − + Ω −

energy density pressure

diag( , , , )pT p p pµ

ν

ρ

ρ

==

=

Robertson-Walker metric Perfect-fluid stress tensor

8G GTµν µνπ=

Field equationsField equationsField equations

( )

2

2

2 =expansion rate

1 =deceleration paramet

8 3

4 er3 3

a k Ga aa G pa

aHaaqa H

π ρ

π ρ

+ =

=

≡

−− + ≡

whateverM Rρ ρ ρ ρΛ= + + +

3(1 )whatever: ww w wp w w p aρ ρ ρ − += = ∝

0vacuum: 1 p w aρ ρΛ Λ Λ= − = − ∝

4radiation: 3 1 3 R R Rp w aρ ρ −= = ∝

3matter: 0 0 M Mp w aρ −= = ∝

dist

ance

age of the universe

Cosmological constant (dark energy)Cosmological constant (dark energy)Cosmological constant (dark energy)

dark matter dominant

dark energy dominant

expands foreverever slowing

collapses

Hubble’s Discovery Paper - 1929Hubble’s Discovery Paper Hubble’s Discovery Paper -- 19291929s

-1 -10 100 km s MpcH h=

0 0v ( Hubble's constant)H d H= =

5h =

University of Chicago 1909 National Champions

0.72 .03 .07 Freedman et al. (Hubble Key Project)0.57 .02 Sandage, Tammann, et al.

hh

= ± ±= ±

Riess et al astro-ph/9410054

Hubble’sdata

1917 Einstein proposescosmological constant

1929 Hubble discoversExpansion of the universe

1934 Einstein calls it“my biggest blunder”

1998 Astronomers findevidence for it

Einstein’sBiggest Blunder?

Einstein’sEinstein’sBiggest Blunder? Biggest Blunder?

ΛΛΛ12 8R g R g GTµν µν µν µνπ− − Λ =

( )diag , , ,T p p pµν ρ= − − −

( )diag , , , 8T Gµν ρ ρ ρ ρ ρ πΛ Λ Λ Λ Λ= = Λ

“I found it very ugly indeed that the field law of gravitation should be composed of two logically independent terms connected by addition. About the justification of such feelings concerning logical simplicity it is difficult to argue. I cannot help to feel it strongly and I am unable to believe that such an ugly thing should be realized in nature.”

Einstein in a letter to Lemaitre, Sept. 26, 1947

Field equation:

Perfect fluid stress tensor:

( )12 8R g R G T Tµν µν µν µνπ− = +

Modern view: “It belongs on the right-hand side,and has many contributions.”

2 20

22 2 2 2 2 2 2

02

4 = area of centered on source at time of detection,

( ) Area 4 ( )1

Ld S t

drds dt a t r d a t rkr

π

π

= − + Ω ⇒ = −

0

1light from comoving coordinate at time t reaches us now by an amountredshifted (1 ) ( ) ( ) z a t

ra t+ =

luminosity distance defines - "know" , measure 2L

LF = L F4 dπ

( ) ( )2 2

2

Conservation of energy: flux redshifted:

redshift of energy redshift of time interva

(1 )

: ) l (1 0 1= a t az t

z

+×

+

002 2 2

(1 )4 (( ) (1 )

) LzLF =

a t rd a t r z

π += +⇒

Distance-redshift relationDistanceDistance--redshiftredshift relationrelation

0( ) (1 )Ld a t r z= +2

2 2 2 2 22( )

1drds dt a t r dkr

= − + Ω −

22 ( ) ( )1dr dt da

a t H a akr= =

−∫ ∫ ∫light travels on geodesics

2 0ds =

2 2 2 30 TOTAL(1 )(1 ) (1 ) ...MH H z z = − Ω + + Ω + +

( )20

TOTAL TOTAL

3 8

... (1 )i i

M R w

H G

k

ρ π

Λ

Ω =

Ω = Ω + Ω + Ω + Ω + − Ω ∝

1 10 0

2 2 3 3(1 )0 00

( ) 1 (1 )(1 ) (1 ) (1 ) ...

r z

wM w

a t H dzdrkr z z z

− −

+

′′=

′ ′ ′ ′− − Ω + + Ω + + Ω + +∫ ∫

Distance-redshift relationDistanceDistance--redshiftredshift relationrelation

Distance-redshift relationDistanceDistance--redshiftredshift relationrelation

0( ) (1 )Ld a t r z= +

1 10 0

0 2 2 30 0TOTAL

( ) ( ) from 1 (1 )(1 ) (1 ) ...

r z

M

a t H dzdra t rkr z z

− − ′′=

′ ′ ′− − Ω + + Ω + +∫ ∫

Example: matter + lambda TOTAL M ΛΩ = Ω + Ω

LdProgram:• measure (via ) and • input and calculate

2 / 4Ld L Fπ=

iΩ 0( )a t r

20 ( )

L

i

H d z O z= +Ω ↵

z

• Luminosity distance

• Angular diameter distance

• Comoving volume element

• Age of the universe

Evolution of H(z) is a key quantityEvolution of Evolution of H(zH(z) is a key quantity) is a key quantityIn a flat universe, many measures based on the comoving distance ( ) ( )0

z dzr zH z

= ∫

( ) ( )( )1Ld z r z z= +

( ) ( )( )1A

r zd z

z=

+

( )( )

( )( )

2dV z r zdzd z H z

=Ω

( ) ( ) ( )0

11

z

t z dzz H z

=+∫

Lum

inos

ity /

Sola

r Lum

inos

ity

10

9

9

8

10

4 10

1.6 10

6.4 10

×

×

×-20 0 20 40 60

days

Type Ia Supernovae(not calibrated)

Type Ia supernovaType Type IaIa supernovasupernovaSupernova Cosmology Project

Lum

inos

ity /

Sola

r Lum

inos

ity

10

9

9

8

10

4 10

1.6 10

6.4 10

×

×

×

Type Ia Supernovae(calibrated)

-20 0 20 40 60days

Type Ia supernovaType Type IaIa supernovasupernovaSupernova Cosmology Project

appa

rent

mag

nitu

de [l

og(d

ista

nce)

]Type Ia supernovaType Type IaIa supernovasupernova

resi

dual

s (m

agni

tude

s)Type Ia supernovaType Type IaIa supernovasupernova

High-z SNeIa are fainter than expected in an Einstein-deSitter model

cosmological constant, or…some changing non-zero vacuum energy, or… or some unknown systematic effect(s)

ΩMATTER

ΩVA

CU

UM

maximumtheoretical

bliss

The case for Λ:1) Hubble diagram

3) age of the universe4) structure formation

2) subtractionΩ TOTAL= 1ΩΜ = 0.31 − 0.3 = 0.7

Theorist’s Theorist’s view of the view of the universeuniverse

(isotropic)(isotropic)

Temperature of the universeTemperature of the universeTemperature of the universe

2 52.5 10hγ−Ω = ×

100σ error bars

Observer’s Observer’s view of the view of the universeuniverse

(fluctuations)(fluctuations)

( , ) ( , )lm lmT a Yδ θ φ θ φ= ∑

Angular power spectrum Angular power spectrum Angular power spectrum

2 2( , )Tδ θ φ1 1( , )Tδ θ φ

2l lmC a≡

Acoustic peaksAcoustic peaksAcoustic peaks• At recombination, baryon−photon fluid undergoes“acoustic oscillations”

• Compressions and rarefactions change • Peaks in correspond to extrema of

compressions and rarefactions• Multipole number corresponds to a

physical length scale

cos sinA kt B kt+Tγ

Tγ∆

Hu

Acoustic peaksAcoustic peaksAcoustic peaksSound travel distance knownObserved lpeak ~ geometry

Flat (Euclidean)

Spherical (closed)

Hyperbolic (open)

TOTAL 1 0.1Ω = ±

WMAPWMAPWMAP

David T. Wilkinson1935-2002

WMAP science teamWMAP model

WMAP Angular Power SpectrumWMAP Angular Power SpectrumWMAP Angular Power SpectrumTOTAL 1.02 0.02Ω = ±

QSO 1937-1009

Ly−α

Burles et al.Tytler

Baryons ΩB h2∼ 0.02BaryonsBaryons ΩΩB B hh22∼ 0.02∼ 0.02

2BWMAP: 0.0224 0.0009hΩ = ±

dynamics

x-ray gas

lensing

Matter ΩM ∼ 0.3MatterMatter ΩΩM M ∼ 0.3∼ 0.3

power spectrum

ΩTOTAL = 1, ΩΜ = 0.3 1 − 0.3 = 0.7

M33 rotation curve

105

100

50

expectedfromluminous disk

observed

• galaxy & cluster dynamics• gravitational lensing• structure formation• CMB observations

v (k

m/s

)

R (kpc)

Sofue & Rubin

Rotation curvesRotation curvesRotation curvesCO – central regionsOptical – disksHI – outer disk & halo

Observer’s view of the universeObserver’s view of the universe

lumpy (inhomogeneous and anisotropic) full of stars, galaxies, clusters, ….

NGC 6070NGC 6070

Theorist’s view of the universeTheorist’s view of the universe

smooth (homogeneous and isotropic) full of dark matter (and dark energy)

Actual image of dark matterActual image of dark matter

• Assume there is an average density

• Expand density contrast in Fourier modes

• Autocorrelation function defines power spectrum

Power spectrumPower spectrumPower spectrum

( ) ( ) ( ) 3exp k

xx ik x d k

ρ ρδ δ

ρ−

≡ = − ⋅∫

2 3 2

20

( ) ( ) ( ) 2

kkx dkx xk

δδρ δ δρ π

∞

= = ∫

ρ

( )xδ

3 22 2

2( ) ( )2

kk

kk P k

δδ

π∆ ≡ ≡

Harrison-Zel’dovichSpectrum

HarrisonHarrison--Zel’dovichZel’dovichSpectrum Spectrum

Tegmark

0.25 0.05 0.25 1 0.250.25 0.35 0.70

M M

M

h hh

Ω ΩΓ Ω ±∼ ∼

2dF data

Pow

er s

pect

rum

Shape factor

High-z SNeIa are fainter than expected in an Einstein-deSitter model

cosmological constant, or…some changing non-zero vacuum energy, or… or some unknown systematic effect(s)

ΩMATTER

ΩVA

CU

UM

maximumtheoretical

bliss

The case for Λ:1) Hubble diagram

3) age of the universe4) structure formation

2) subtractionΩ TOTAL= 1ΩΜ = 0.31 − 0.3 = 0.7

t0 : age of the universett00 : age of the universe: age of the universe

1

0 1 30 TOTAL

TOTAL

1 www

M

dxH tx− +

Λ

=− Ω + Ω

Ω = Ω + Ω

∫ ∑

Example: matter + lambda TOTAL M ΛΩ = Ω + Ω

Integrate Friedmann equation:

1.00.3

13.5 2 Gyr±

Chaboyer (2001)

13.50.70.3Flat

120 0.3Open9.301.0Flat

0.2

0.2

ΩM

140Open

150.8Flat

t0 (Gyr)ΩΛH0 =70

t0 : age of the universett00 : age of the universe: age of the universe• white dwarf cooling

• nucleocosmochronology

• globular cluster evolution

Cayrel (2001)

12.6 3 Gyr±

First measurement of stellar uranium

12.6 3 Gyr±

13.5 2 Gyr±

ClustersGalaxiesStarsPlanetsPoodlesPigeons Pond Scum...

Everything in the universe:Everything in the universe:Everything in the universe:

From inflationary perturbationsFrom inflationary perturbationsFrom inflationary perturbations

Donald Rumsfeld

Silk damping of baryon pert’nsSilk damping of baryon Silk damping of baryon pert’nspert’ns

ΛCDM(2dF)

Cosmo-illogical constantCosmoCosmo--illogical constantillogical constantMass density of space:

Who ordered that?

30 -3

13 4

4 4

4 4

10 g cm(10 GeV)(10 eV)(10 cm)

ρ −

−

−

− −

ν

ν

ν

Heavy Elements: Ω=0.0003

Cold Dark Matter: Ω=0.25

Dark Energy (Λ): Ω=0.70

Stars:Ω=0.005

Free H & He:Ω=0.04

CRITICAL

TOTAL 1i iρ ρΩ ≡

Ω =

Cosmic PieCosmic PieCosmic Pie

ΛCDMΛΛCDMCDM

Neutrinos (ν): Ω=0.0047

The cosmic food chain (Ωi )The cosmic food chain The cosmic food chain ((ΩΩii ))Massless neutrinos (2) : 0.002%

Photons: 0.005%

Metals: 0.023%

Massive Neutrino (1) m= 0.2 eV: 0.47 %

Stars: 0.50 %

Dark neutrons & protons: 4. %

Dark matter: 25. %

Dark energy: 70. %

Cosmological standard modelCosmological standard modelCosmological standard modelCDMΛ

TOTAL

CDM

B

0.7 1 21

2 / 3 1/ 3 0.04 0.005 0.00005

h

ν

γ

Λ

Ω =ΩΩΩΩΩ

iiiii

Cosmological parameters Initial perturbations

Harrison-Zel’dovich(adiabatic curvatureperturbations with

an initial n=1 spectrum)

Dark Matter and Dark EnergyDark Matter and Dark Energy

Rocky I: Evidence for dark matter and dark energy Rocky II: Dark matter candidatesRocky III: Dark energy reloaded

SLAC Summer Institute, August 2003Rocky Kolb, Fermilab & The University of Chicago